Update Notice (v2) 2026/2/13 This preprint has been superseded by a significantly revised version, which has been uploaded as a separate submission. In the original version (v1), the relation between internal dissipation power and the energy relaxation rate was introduced in a phenomenological manner. However, a rigorous first-principles derivation has now been completed in a companion paper [Guo (2026), Exact Relation between Internal Dissipation Power and Energy Relaxation Rate——A Rigorous Derivation in Markovian Quantum Systems]. Using this exact relation Rinternal=ℏωqΓ1⟨σ+σ−⟩Rinternal=ℏωqΓ1⟨σ+σ−⟩, the previously phenomenological "energy competition" framework has been reformulated from the ground up. As a result: The parameter ff (energy allocation fraction) is now rigorously defined in terms of experimentally accessible quantities, rather than introduced as a phenomenological fit parameter. The previous phenomenological arguments and associated experimental discussions in v1 are no longer valid and should be disregarded. The new version provides a complete microscopic foundation for the theory of energy competition in superconducting qubit decoherence. Readers are strongly encouraged to consult the latest version (available at [10.5281/zenodo.18624328) for a comprehensive and self-contained treatment. Version 2 The decoherence time of superconducting qubits is commonly believed to be dominatedby dielectric loss (loss tangent tan 𝛿). Multiple experimental studies have found an empiricalscaling relationship approximately Γ ∝ (tan 𝛿)0.7 between the decoherence rate Γ = 1/𝑇2and tan 𝛿. Based on the ”Interface Projection Realism” framework, this paper proposes apossible new physical picture for decoherence. By analyzing 25 superconducting quantumdevices covering single-qubit, multi-qubit, hybrid systems, and 3D integration, we observethe dispersion of this scaling relationship in optimized interface samples. Experimentaldata show that unoptimized samples indeed follow Γ ∝ (tan 𝛿)0.7, while optimized samplesexhibit significant dispersion in the scaling exponent.To explain this phenomenon, we propose a decoherence theoretical framework basedon the ”Energy Competition” picture. This framework reinterprets decoherence as the re-sult of competitive allocation of the input microwave energy between the ”internal dissipa-tion channel generating noise” and the ”net channel maintaining coherence.” This physicalpicture is a concrete implementation of Interface Projection Realism in the decoherenceproblem. By introducing the energy allocation ratio 𝑓 and the interface intrinsic competi-tion coefficient 𝜒, the theoretical framework predicts that the pure dephasing rate satisfiesΓ𝜙 = 𝜒 · 𝑓 /(1 − 𝑓 ) in the strong suppression limit. This framework provides a possibleexplanation for the dispersion of scaling behavior. Furthermore, the analysis of paired sam-ples (with the same tan 𝛿 but 𝑇2 differing by a factor of 16.7) provides indirect evidence forthe possibility of 𝑓 being an independent parameter.Moreover, the theoretical framework can unify the explanation of decoherence data fromsingle qubits to complex systems and proposes unique predictions that can be directly veri-fied experimentally, such as power independence and noise spectrum evolution. This workprovides a new perspective based on Interface Projection Realism for understanding quan-tum decoherence and deepens the goal of interface engineering from simply reducing lossto possibly regulating the energy allocation ratio 𝑓 . Important Update (Updated January 28, 2026) The square-root decoherence scaling law (Γ∝κeff) with scaling exponent α=0.5 reported in this work was derived via empirical fitting against superconducting qubit experimental datasets, based on the "resource competition theory at dynamic projection interfaces." This exponent was established under the framework of phenomenological analysis, leveraging established physical heuristics for intrinsic material loss and the loss angle tanδ, and exhibited high fitting goodness for low-noise, weak-coupling quantum systems. Subsequent research has advanced this framework to a comprehensive mathematical-physical theory—Interface Projection Realism (IPR)—grounded in quantum information first principles. A key innovation of IPR is the introduction of the transmissivity field Ξ(x,t) (as the fundamental order parameter describing the quantum-classical interface) and the rigorous derivation of its quantum information dynamics equation. By analyzing an expanded set of superconducting qubit decoherence data through weighted least-squares fitting (yielding R2=0.9987, an extremely significant F-statistic of 2856.3), the universal decoherence scaling exponent is refined to α=0.792±0.008. This revised exponent corresponds to a synergy index m=4.81±0.15, which originates from the cooperative effect of five major noise channels (dielectric loss, quasiparticle tunneling, flux noise, charge noise, and radiation loss) embedded in quantum channel dynamics. IPR further makes two independent testable predictions—equivalence principle violation (Δa/aˉ∼2.3×10−9) and a first-principles calculation of dark energy density (ρΛ≈4.2×10−47GeV4, consistent with Planck 2018 observations)—demonstrating its explanatory power across quantum decoherence, quantum gravity, and cosmology. A complete account of the theoretical derivation, microphysical mechanism, and experimental corroboration is provided in our latest work: Interface Projection Realism: A Multiscale Unified Theory Based on Quantum Information Dynamics (Zenodo, Version v3, DOI: 10.5281/zenodo.18400122, January 28, 2026). This preprint serves as a foundational stage-specific contribution to the evolutionary trajectory of the IPR framework. The α=0.5 square-root scaling relation remains a valid limiting case for low-noise, weak-coupling material systems, while the refined α=0.792 exponent offers a universal description across broader material and noise conditions. Version 1 We report a universal square-root scaling law between the decoherence rate Γ of a quantum system and its effective intrinsic dissipation κeff, i.e., Γ ∝ √ κeff. This empirical law, observed across platforms like superconducting qubits, finds its mechanistic explanation within a new theoretical framework of resource com petition at a dynamic projection interface. The framework posits that our (3+1)-dimensional classical spacetime emerges from a higher-dimensional realm of potentialities (L1) through a filtering process governed by the interface perme ability field Ξ(x, t). Finite information-energy flux from L1 is contested between systems’ tendency to maintain quantum coherence and their intrinsic demand to dissipate noise for classical stability, quantified by κeff. From this competition dy namics, we derive the square-root scaling law. The model further provides unified, objective descriptions of quantum measurement as channel locking and of grav ity as emergence from Ξ-field distortion. Several concrete, testable predictions are proposed, including nonlinear jumps in coherence at phase transitions and a novel testable correlation for equivalence principle experiments.
Update Notice (v2) 2026/2/13 This preprint has been superseded by a significantly revised version, which has been uploaded as a separate submission. In the original version (v1), the relation between internal dissipation power and the energy relaxation rate was introduced in a phenomenological manner. However, a rigorous first-principles derivation has now been completed in a companion paper [Guo (2026), Exact Relation between Internal Dissipation Power and Energy Relaxation Rate——A Rigorous Derivation in Markovian Quantum Systems]. Using this exact relation Rinternal=ℏωqΓ1⟨σ+σ−⟩Rinternal=ℏωqΓ1⟨σ+σ−⟩, the previously phenomenological "energy competition" framework has been reformulated from the ground up. As a result: The parameter ff (energy allocation fraction) is now rigorously defined in terms of experimentally accessible quantities, rather than introduced as a phenomenological fit parameter. The previous phenomenological arguments and associated experimental discussions in v1 are no longer valid and should be disregarded. The new version provides a complete microscopic foundation for the theory of energy competition in superconducting qubit decoherence. Readers are strongly encouraged to consult the latest version (available at [10.5281/zenodo.18624328) for a comprehensive and self-contained treatment. Version 2 The decoherence time of superconducting qubits is commonly believed to be dominatedby dielectric loss (loss tangent tan 𝛿). Multiple experimental studies have found an empiricalscaling relationship approximately Γ ∝ (tan 𝛿)0.7 between the decoherence rate Γ = 1/𝑇2and tan 𝛿. Based on the ”Interface Projection Realism” framework, this paper proposes apossible new physical picture for decoherence. By analyzing 25 superconducting quantumdevices covering single-qubit, multi-qubit, hybrid systems, and 3D integration, we observethe dispersion of this scaling relationship in optimized interface samples. Experimentaldata show that unoptimized samples indeed follow Γ ∝ (tan 𝛿)0.7, while optimized samplesexhibit significant dispersion in the scaling exponent.To explain this phenomenon, we propose a decoherence theoretical framework basedon the ”Energy Competition” picture. This framework reinterprets decoherence as the re-sult of competitive allocation of the input microwave energy between the ”internal dissipa-tion channel generating noise” and the ”net channel maintaining coherence.” This physicalpicture is a concrete implementation of Interface Projection Realism in the decoherenceproblem. By introducing the energy allocation ratio 𝑓 and the interface intrinsic competi-tion coefficient 𝜒, the theoretical framework predicts that the pure dephasing rate satisfiesΓ𝜙 = 𝜒 · 𝑓 /(1 − 𝑓 ) in the strong suppression limit. This framework provides a possibleexplanation for the dispersion of scaling behavior. Furthermore, the analysis of paired sam-ples (with the same tan 𝛿 but 𝑇2 differing by a factor of 16.7) provides indirect evidence forthe possibility of 𝑓 being an independent parameter.Moreover, the theoretical framework can unify the explanation of decoherence data fromsingle qubits to complex systems and proposes unique predictions that can be directly veri-fied experimentally, such as power independence and noise spectrum evolution. This workprovides a new perspective based on Interface Projection Realism for understanding quan-tum decoherence and deepens the goal of interface engineering from simply reducing lossto possibly regulating the energy allocation ratio 𝑓 . Important Update (Updated January 28, 2026) The square-root decoherence scaling law (Γ∝κeff) with scaling exponent α=0.5 reported in this work was derived via empirical fitting against superconducting qubit experimental datasets, based on the "resource competition theory at dynamic projection interfaces." This exponent was established under the framework of phenomenological analysis, leveraging established physical heuristics for intrinsic material loss and the loss angle tanδ, and exhibited high fitting goodness for low-noise, weak-coupling quantum systems. Subsequent research has advanced this framework to a comprehensive mathematical-physical theory—Interface Projection Realism (IPR)—grounded in quantum information first principles. A key innovation of IPR is the introduction of the transmissivity field Ξ(x,t) (as the fundamental order parameter describing the quantum-classical interface) and the rigorous derivation of its quantum information dynamics equation. By analyzing an expanded set of superconducting qubit decoherence data through weighted least-squares fitting (yielding R2=0.9987, an extremely significant F-statistic of 2856.3), the universal decoherence scaling exponent is refined to α=0.792±0.008. This revised exponent corresponds to a synergy index m=4.81±0.15, which originates from the cooperative effect of five major noise channels (dielectric loss, quasiparticle tunneling, flux noise, charge noise, and radiation loss) embedded in quantum channel dynamics. IPR further makes two independent testable predictions—equivalence principle violation (Δa/aˉ∼2.3×10−9) and a first-principles calculation of dark energy density (ρΛ≈4.2×10−47GeV4, consistent with Planck 2018 observations)—demonstrating its explanatory power across quantum decoherence, quantum gravity, and cosmology. A complete account of the theoretical derivation, microphysical mechanism, and experimental corroboration is provided in our latest work: Interface Projection Realism: A Multiscale Unified Theory Based on Quantum Information Dynamics (Zenodo, Version v3, DOI: 10.5281/zenodo.18400122, January 28, 2026). This preprint serves as a foundational stage-specific contribution to the evolutionary trajectory of the IPR framework. The α=0.5 square-root scaling relation remains a valid limiting case for low-noise, weak-coupling material systems, while the refined α=0.792 exponent offers a universal description across broader material and noise conditions. Version 1 We report a universal square-root scaling law between the decoherence rate Γ of a quantum system and its effective intrinsic dissipation κeff, i.e., Γ ∝ √ κeff. This empirical law, observed across platforms like superconducting qubits, finds its mechanistic explanation within a new theoretical framework of resource com petition at a dynamic projection interface. The framework posits that our (3+1)-dimensional classical spacetime emerges from a higher-dimensional realm of potentialities (L1) through a filtering process governed by the interface perme ability field Ξ(x, t). Finite information-energy flux from L1 is contested between systems’ tendency to maintain quantum coherence and their intrinsic demand to dissipate noise for classical stability, quantified by κeff. From this competition dy namics, we derive the square-root scaling law. The model further provides unified, objective descriptions of quantum measurement as channel locking and of grav ity as emergence from Ξ-field distortion. Several concrete, testable predictions are proposed, including nonlinear jumps in coherence at phase transitions and a novel testable correlation for equivalence principle experiments.
Important Update on March 9, 2026: In this version, the description of environmental effects has been corrected: they are now properly treated as encapsulated within the effective spectral density of the interfacial defect network D, rather than as direct driving terms. All core results and conclusions remain unchanged, but the physical interpretation is refined to align with the energy distribution framework introduced in Part II of this series. Version 2 This paper is the third in the "Interface-Projected Realism" series. This series of work aims to establish a new theoretical paradigm: Ontologically, replace probabilistic wave function descriptions with deterministic energy flow; Methodologically, redefine physical reality as an interactive whole composed of quantum units (Q), an interfacial defect network (D), and bulk channels (B). In the first work, an exact relationship between energy flow and relaxation rate was established, providing a formal bridge for the paradigm shift. In the second work, the "Energy Distribution Framework" was proposed, demonstrating that dissipation is the deterministic allocation of energy between Q and D, and deriving the universal formula for internal dissipation power Rint=ℏωq[Γ↓⟨n⟩−Γ↑(1−⟨n⟩)], where the relaxation rates are completely determined by the internal structure of D, revealing the core role of the energy distribution ratio f. This paper generalizes this new paradigm based on energy distribution from single-body to many-body systems. The core step is to define multiple Q contacts and their shared D and B together as a new, unified composite system. Within this framework, the traditionally complex "many-body correlated dissipation" is clearly interpreted as a macroscopic result of the deterministic flow of energy within this composite system, governed by allocation and transport rules determined by the structure of the D network. Through rigorous coarse-graining of this overall system, this paper derives the governing equation for the evolution of its internal energy density field u(r,t)—a classical reaction-diffusion equation:∂t∂u=Rtotal−γ0(r)u+∇⋅(γ2∇u).Here, the local dissipation rate γ0(r) and the diffusion coefficient γ2 are completely determined by the properties of the D network, corresponding respectively to the spatial distribution of the energy distribution ratio f from the second paper and the redistribution effect induced by its correlations. This theory is not only logically self-consistent but also provides a unified explanation for multiple cutting-edge experiments. This paper marks that a physical framework based on deterministic energy distribution and transport can now systematically describe many-body correlation phenomena, providing crucial support for the completeness of the new paradigm. \textbf{Keywords}: Interface-Projected Realism; Energy Distribution; Many-Body Systems; Correlated Dissipation; Reaction-Diffusion Equation Version 1 Traditional quantum theory typically attributes energy dissipation to random perturbations from the external environment. Based on the "Interfacial Projected Realism" framework, this work re-examines the nature of energy dissipation from a novel perspective, treating the qubit, the interfacial defect network, and the bulk dissipation channel as a self-contained total system. We first rigorously derive the universal formula for internal dissipation power and the energy distribution ratio f in single-body quantum systems, and then extend these concepts to many-body systems. Starting from a microscopic Hamiltonian coupling multiple qubits to a common quantized field and employing the Nakajima-Zwanzig projection operator technique, we obtain a universal expression for the energy dissipated from a many-body system to the environment. Applying this result to the specific model of multiple two-level systems coupled to a common bosonic field yields a collective master equation where the dissipation coefficient matrix Γij encodes all spatial and coupling information. Through systematic coarse-graining, gradient expansion, and semiclassical approximation, we derive for the first time from an energy-distribution perspective a closed set of macroscopic equations for the local system energy density u(r,t) and the environmental field energy density U(r,t): ∂t∂u=Rtotal(r,t)−γ0(U)u+∇⋅(γ2(U)∇u)∂t∂U=D∇2U−ΓBU+ρ(r)γ0(U)u Within this framework, the energy distribution ratio f(r,t)=γ0u/Rtotal emerges naturally as a macroscopic quantity, its physical essence being jointly determined by the system’s microscopic coupling structure (embodied by Γij) and quantum statistical state. The theory quantitatively explains several long-unexplained anomalous phenomena in cutting-edge experiments, demonstrates strong testability, and lays a solid foundation for exploring deeper connections between energy distribution and macroscopic physics. For the exact mathematical formulation and detailed derivations, please refer to the PDF file.
Based on the "Interface Projection Realism" framework, this paper rigorously derives the universal formula for internal dissipation power and the microscopic expression for the energy distribution ratio f from first principles. We treat the qubit (Q), the interfacial defect network (D), and the bulk dissipation channel (B) as a self-contained total system, no longer presupposing any part of it as an external environment. By applying the Born-Markov approximation to the degrees of freedom of D and B, we obtain the reduced master equation for Q, and subsequently calculate the net energy flow rate from Q to the incoherent degrees of freedom—the internal dissipation power R_internal. The result is: R_internal = ħω_q [Γ↓ ⟨n⟩ - Γ↑ (1-⟨n⟩)], where Γ↓ and Γ↑ are transition rates determined by the Q-D coupling and the internal structure of D, and ⟨n⟩ is the excited state population of Q. This formula does not rely on any thermal equilibrium assumptions and is applicable to arbitrary Markovian non-equilibrium steady states. Building on this, we define the total effective power absorbed by the system as R_total = ⟨∂H_drive/∂t⟩ and introduce the system's stored energy E_stored = ⟨H_Q⟩. Under periodic averaging, the energy conservation equation reads dE_stored/dt = R_total - R_internal, where the overline denotes time average. The energy distribution ratio f = R_internal / R_total satisfies f = 1 in the periodic steady state where dE_stored/dt = 0; during transients, f can deviate from 1, its specific expression depending on microscopic parameters, reflecting the degree of deviation from the steady state. We further demonstrate that when D and B are in thermal equilibrium, the above formula reduces to the traditional fluctuation-dissipation theorem. This paper proves that the universal formula for internal dissipation power naturally contains the fluctuation-dissipation theorem under thermal equilibrium conditions, while its validity in non-equilibrium states constitutes a non-equilibrium generalization of the traditional theorem, providing a unified theoretical foundation for understanding the energetic origin of quantum decoherence.
This paper rigorously proves the exact relation between the internal dissipation power Rinternal (the net power flowing from the system to the dissipative channel) and the energy relaxation rate Γ1 for a broad class of Markovian quantum systems. Starting from the standard Lindblad master equation incorporating an amplitude damping term, we provide a purely algebraic proof that, in the absence of driving and at zero temperature, the identity Rinternal = ℏωqΓ1⟨σ+σ−⟩ holds universally. This proof does not rely on any additional assumptions regarding the microscopic origin of Γ1 or the strength of pure dephasing. For systems subject to external driv ing, we precisely define the internal dissipation power according to the first law of quantum thermodynamics, and we provide a completely self-contained demon stration that, under the original driving form without invoking the rotating-wave approximation, the exact result is Rinternal = ℏωqΓ1⟨σ+σ−⟩ + ℏ 2 ΩΓ1 cos(ωdt)⟨σx⟩; this correction term originates from counter-rotating components and, under the rotating-wave approximation, averages to zero over time due to its fast oscilla tion, thereby recovering the same relation as in the undriven case. For finite temperature environments, we derive the modified relation Rinternal = ℏωqΓ1 [ (1+ 2nth)⟨σ+σ−⟩ − nth] and verify that it vanishes in thermal equilibrium. This arti cle elaborates on the minimal assumptions, conditions of independence, and limitations of this relation, and also presents its generalization to multi-level sys tems.
⚠️ IMPORTANT: This manuscript is deprecated. The decoherence experiments designed based on the earlier framework presented here have been fundamentally revised and superseded by a rigorous derivation from first principles. Please refer to the corrected framework:[Exact Relation between Internal Dissipation Power and Energy Relaxation Rate: A Rigorous Derivation in Markovian Quantum Systems]DOI: 10.5281/zenodo.18624328Zenodo: https://zenodo.org/records/18624328 Version1: Quantum decoherence is a fundamental physical process connecting quantum theory with the classical world. Standard decoherence theory predicts that quan tum coherence decays exponentially to zero under strong environmental perturba tions. However, whether the complex Hilbert space structure of high-dimensional quantum systems leads to deviations from this standard picture remains an open frontier question. This paper presents a systematic experimental framework to dis criminate and separate three potential decoherence mechanisms in high-dimensional photon orbital angular momentum systems: standard Markovian decoherence (H0), non-Markovian memory effects (HNM), and potential non-classical behavior (H1). The scheme employs dual criteria of “noise spectrum fingerprint” and “environ mental control,” combined with Bayesian model comparison, forming a closed-loop mechanism diagnostic workflow. Theoretical analysis indicates that when system Hilbert space dimension reaches a critical range (d ≥ 7), non-classical behaviors may emerge: visibility saturation at a non-zero value under strong decoherence (Vsat ≈ 0.25), accompanied by non-monotonic revival of entanglement measure with increasing dimension. This work’s primary contribution is its methodologi cal innovation—establishing a generalizable, rigorous framework for discriminating competitive decoherence mechanisms in complex quantum systems.
Preprint: This paper derives quantitative bounds on measurement windows for finite-capacity observers extracting information from decohering quantum systems, extending standard decoherence theory to realistic experimental constraints. Main Result: For Gaussian-Markovian decoherence with exponential information decay I(t) = I₀ exp(-2Γt), bounded-capacity observers lose access to system distinctions when mutual information drops below detection threshold ε, yielding measurement window: τ_c = (1/2Γ) log(α C_A / ε) where Γ is decoherence rate [s⁻¹], C_A is observer capacity [bits] defined via Shannon formula (bandwidth × log₂(SNR) × integration time), ε is detection threshold [bits], and α ~ 0.1-1 is a model-dependent constant from spectral decomposition of environmental information. This establishes logarithmic capacity-scaling: doubling detector quality extends measurement windows by only ~0.35/Γ seconds, implying diminishing returns from capacity improvements. Experimental Predictions: For state-of-the-art circuit QED (superconducting transmon qubits, T₁ = 100 μs, bandwidth Δf = 10 MHz, SNR = 10), the framework predicts τ_c ~ 4-10 μs. Varying bandwidth from 1-30 MHz (capacity C_A ∈ [3, 90] bits) produces measurable Δτ_c ≈ 1.7 μs variation (5-10% of coherence time). Five experimental tests discriminate capacity-scaling from standard decoherence: ∙ Tests 1-3: Verify logarithmic capacity-scaling, inverse rate-dependence, threshold-dependence ∙ Test 4: Multi-observer non-redundancy (at most one narrowband detector succeeds) ∙ Test 5: Capacity-dependent redundancy buildup (primary discriminating signature) Key Contributions: ∙ First quantitative analysis of Zurek's pre-objective phase under explicit finite-resource constraints ∙ Capacity-scaling law connecting Shannon information theory to quantum measurement dynamics ∙ Operational definitions ensuring falsifiability (capacity, threshold, mutual information defined via measurement protocols) ∙ Concrete numerical predictions for three platforms (circuit QED, spin qubits, optomechanics) with resource estimates ∙ Design principle: environmental shielding (linear benefit in τ_c) outperforms detector improvement (logarithmic benefit) when both options available Technical Approach: The bound follows from threshold-crossing analysis of exponential decay with capacity-limited initial information I₀ = α C_A, justified via spectral decomposition of environmental information under flat-spectrum approximation for narrowband observation. All parameters (Γ, C_A, ε) are operationally defined and independently measurable, avoiding circularity. Extensions to non-Markovian dynamics (memory kernels), scrambling systems (black holes, many-body chaos), and non-Gaussian noise (Lévy flights, 1/f noise) are discussed with conjectured scaling laws. Scope: The bound applies specifically to Gaussian-Markovian systems (harmonic oscillators, qubits in dispersive limit, weak continuous measurement with memoryless baths). Circuit QED provides optimal testbed due to tunable Purcell filters (bandwidth control), high coherence times (T₁ > 300 μs achieved), and multiplexed readout infrastructure (5+ independent detectors demonstrated). Validity requires α C_A > ε (initial information exceeds threshold); domain violations occur when capacity too small, threshold too high, or coupling too weak. Relation to Prior Work: Zurek's Quantum Darwinism (2003-2009) explains asymptotic objectivity emergence through environmental redundancy but assumes unbounded observers (C_A → ∞, t → ∞). This work analyzes the complementary finite-resource regime (C_A < ∞, t ~ τ_c), providing first capacity-parameterized bound on pre-objective phase duration. Framework is interpretation-neutral—compatible with Copenhagen, Many-Worlds, Bohmian mechanics, and relational quantum mechanics. Philosophical implications (process ontology, observer-dependent reality, impermanence) are explored but clearly separated from testable predictions. Methods: Open quantum systems theory, Shannon information theory, operational quantum measurement, circuit QED experimental physics, numerical prediction for realistic parameters. Content: Complete 90-page manuscript with axiomatic framework (§2), narrowband observation model (§3), main theorem with proof (§4), numerical predictions (§5), five experimental falsification tests (§6), detailed Quantum Darwinism comparison (§7), extensions and limitations (§8), interpretive options (§9), and honest assessment (§10). Includes 77 references and operational definitions for all information-theoretic quantities. Target Audience: Quantum foundations researchers, experimental quantum physicists (circuit QED, trapped ions, quantum dots), quantum information theorists, philosophers of physics interested in measurement and objectivity.
The transition from quantum to classical behavior remains one of the fundamental questions in physics. Existing models, such as environmental decoherence, explain how quantum effects diminish in open systems, but a precise energy-based mechanism governing this transition has yet to be fully established. This paper introduces the Orpheus Equation, a novel framework describing how quantum effects suppress as energy accumulates. A rigorous derivation from Schrodinger's equation suggests that quantum suppression follows a power-law decay rather than the traditionally assumed exponential decay. This principle predicts a universal energy-dependent mechanism underlying decoherence.We present explicit numerical estimates for the critical energy scale E_crit in various physical systems, including superconducting qubits, molecular interference experiments, and optomechanical oscillators. Additionally, we examine empirical evidence from molecular and atomic physics that aligns with this theory, including studies on Efimov states, quantum decoherence in atomic systems, single-molecule junctions, and solvation-induced decoherence. These findings suggest that quantum suppression is intrinsically tied to energy accumulation, independent of environmental interactions.Furthermore, we explore the implications of this framework for quantum computing, high-energy quantum systems, and potential links to gravitational decoherence. The Orpheus Equation provides a mathematically and experimentally testable approach to understanding the quantum-classical transition. We propose specific experimental tests and data analysis methods to validate its predictions, positioning this theory as a candidate for bridging quantum mechanics and classical physics.